Answered

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A basketball league's average score is 58 points per game. Coach Ivic Gee tracks a team's average and compares it to the league's average. The table shows the variances in scores for five weeks.

\begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{5}{|c|}{ Points Above/Below Average } \\
\hline Week 1 & Week 2 & Week 3 & Week 4 & Week 5 \\
\hline [tex]$2 \frac{1}{8}$[/tex] & 1.6 & [tex]$-2 \frac{1}{8}$[/tex] & -1.8 & [tex]$-1 \frac{4}{5}$[/tex] \\
\hline \hline
\end{tabular}

Which comparison is true? Use the number line to help you.

A. Week 1 = Week 3
B. Week 4 = Week 5
C. Week 2 < Week 4
D. Week 5 < Week 3

Sagot :

GinnyAnswer
To determine the validity of the comparisons given in the question, let's analyze each statement step-by-step:

### Values Provided
From the table, we have the following variances above or below the average score:

1. Week 1: [tex]\( 2 \frac{1}{8} \)[/tex]
[tex]\[ 2 \frac{1}{8} = 2 + \frac{1}{8} = \frac{16}{8} + \frac{1}{8} = \frac{17}{8} \approx 2.125 \][/tex]
2. Week 2: 1.6
3. Week 3: [tex]\( -2 \frac{1}{8} \)[/tex]
[tex]\[ -2 \frac{1}{8} = - (2 + \frac{1}{8}) = - \left(\frac{16}{8} + \frac{1}{8}\right) = - \frac{17}{8} \approx -2.125 \][/tex]
4. Week 4: -1.8
5. Week 5: [tex]\( -1 \frac{4}{5} \)[/tex]
[tex]\[ -1 \frac{4}{5} = - (1 + \frac{4}{5}) = - \left(1 + 0.8\right) = -1.8 \][/tex]

### Comparison Analysis
1. Week 1 = Week 3:
- Week 1 value: 2.125
- Week 3 value: -2.125
[tex]\[\text{Result: } 2.125 \neq -2.125 \implies \text{False} \][/tex]

2. Week 4 = Week 5:
- Week 4 value: -1.8
- Week 5 value: -1.8
[tex]\[\text{Result: } -1.8 == -1.8 \implies \text{True} \][/tex]

3. Week 2 < Week 4:
- Week 2 value: 1.6
- Week 4 value: -1.8
[tex]\[\text{Result: } 1.6 \not < -1.8 \implies \text{False} \][/tex]

4. Week 5 < Week 3:
- Week 5 value: -1.8
- Week 3 value: -2.125
[tex]\[\text{Result: } -1.8 \not < -2.125 \implies \text{False} \][/tex]

### Summary
- The comparison Week 1 = Week 3 is false.
- The comparison Week 4 = Week 5 is true.
- The comparison Week 2 < Week 4 is false.
- The comparison Week 5 < Week 3 is false.

Therefore, the only true statement is:

Week 4 = Week 5
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